Using an asymptotic analysis, we obtain an eigenvalue equation for the general mode dispersion in Bragg fibers. The asymptotic analysis is applied to calculate the dispersion relation and the field distribution of TE modes in a Bragg fiber. We compare the asymptotic results with exact solutions and find excellent agreement between them. This asymptotic approach greatly simplifies the analysis a...

The basic boundary-contact oscillation problems are considered for a three-dimensional piecewise-homogeneous isotropic elastic medium bounded by several closed surfaces. Using Carleman’s method, the asymptotic formulas for the distribution of eigenfunctions and eigenvalues are obtained. 1. After the remarkable papers of T. Carleman [1–2] the method based on the asymptotic investigation of the r...

Individual data from a continuous distribution are often partitioned into a collection of intervals defined by either fixed interval limits or sample quantiles. In this study, we derive asymptotic distribution of interval statistics for both cases, allowing multiple sample statistics for each interval. Under fixed intervals, the covariance matrix is singular. We identify a computationally simpl...

We study the pion form factor F πγγ ∗ (Q2) in the light-cone sum rule approach, accounting for radiative corrections and higher twist effects. Comparing the results to the CLEO experimental data on F πγγ ∗ (Q2), we extract the the pion distribution amplitude of twist-2. The deviation of the distribution amplitude from the asymptotic one is small and is estimated to be a2(μ) = 0.12± 0.03 at μ = ...

The present article proposes two step-down multiple testing procedures for asymptotic control of the family-wise error rate (FWER): the first procedure is based on maxima of test statistics (step-down maxT), while the second relies on minima of unadjusted p-values (step-down minP). A key feature of our approach is the characterization and construction of a test statistics null distribution (rat...

For population genetics models with recombination, obtaining an exact, analytic sampling distribution has remained a challenging open problem for several decades. Recently, a new perspective based on asymptotic series has been introduced to make progress on this problem. Specifically, closed-form expressions have been derived for the first few terms in an asymptotic expansion of the two-locus s...

We investigate the asymptotic behavior of the OLS estimator for regressions with two slowly varying regressors. It is shown that the possibilities include a definite case, when the third-order regular variation is sufficient to determine the asymptotic distribution, and an indefinite case, when higher-order regular variation is required to find the distribution. In the definite case the asympto...